What does “No dream is ever just a dream” mean in Eyes Wide Shut?

Danny Bowes at Tor.com argues:

Almost nothing in its entire two hours and forty minutes is literally happening, and the audience is given very little warning that this is so, which means if anyone ever invents the genre “stealth fantasy,” Eyes Wide Shut will be its Lord of the Rings trilogy.

He elaborates:

the reason the movie’s pace is a little off is because Stanley Kubrick hadn’t quite finished fine-tuning the editing before he died, or that the novel it’s ostensibly based on, Arthur Schnitzler’s Traumnovelle, is actually the story that’s dreamed by Tom Cruise for 90% of the movie

To be precise:

If Kubrick had survived to make a few more tweaks to the editing, I think it would have been a bit clearer that everything in the movie from when Tom Cruise takes the phone call in the middle of the argument with Nicole Kidman (the argument where it takes Nicole Kidman twenty times longer to say her lines than any human being has ever taken to say the equivalent number of words) to the very end when they take their daughter shopping in FAO Schwartz takes place inside Tom Cruise’s mind. The movie is, after all, based on a book called “Dream Story,” and most of that last conversation between Tom Cruise and the slow-motion Nicole Kidman is concerned with dreams. That part is fairly easy to sort out.

Madison Brek at Film School Rejects points out:

So many things about these shots contribute to this motif of dreams. For one thing, long takes like this have an inherently hypnotic quality. Getting to follow Bill in long and meticulously choreographed shots as he navigates through the beautiful production design is mesmerizing. As the camera moves with him, uninterrupted, we feel as though we’re following him on a journey to god knows where. Often, he is simply aimlessly wandering and our imaginations can run wild. The fact that he’s visiting unconventional, frightening and sometimes outright ridiculous locales adds to the dreaminess as well.

She points out that a real life problem actually contributed to the movie:

Something else that draws you into this atmosphere is the location of filming. Kubrick had a fear of flying. This meant they had to shoot the film in England where he was living at the time. However, Eyes Wide Shut takes place in New York City, which can be a difficult place to replicate. They went to great lengths to reproduce Greenwich Village in an outdoor set at Pinewood studios in England. The final product looks great. However, there is something eerie about the way the setting seems just the slightest bit off. The set looks like New York but still feels inauthentic.

This feeling of being somewhere familiar, but you can’t quite put your finger on what’s wrong, is a common sensation in dreams. Whether or not this was intentional – your guess is as good as mine when it comes to Kubrick – the atmosphere the decision created works well for the final product. The result is that filming at the studio in England adds to the dream state idea and maybe even makes it slightly more nightmarish.

With regards to the quote you mentioned, the author explains:

The earlier mentioned quote comes from Bill and Alice’s final conversation in the film. In their attempt to make amends with one another, they both agree that the “dream” is over. The two cannot erase or ignore last night’s events, but they can choose to move past them. Both characters agree that they’re “awake” now and that that’s all that matters. Bill even promises he will remain that way “forever,” which Alice says she finds to be a frightening idea.